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function L = log_marg_prob_node(CPD, self_ev, pev)
% LOG_MARG_PROB_NODE Compute prod_m log P(x(i,m)| x(pi_i,m)) for node i (linear_gaussian)
% L = log_marg_prob_node(CPD, self_ev, pev)
%
% This differs from log_prob_node because we integrate out the parameters.
% self_ev{m} is the evidence on this node in case m.
% pev{i,m} is the evidence on the i'th parent in case m
% We assume there is <= 1 case.
ncases = length(self_ev);
if ncases==0
L = 0;
return;
elseif ncases==1
y = self_ev{1};
x = cat(1, pev{:}); % column vector
f = 1-x'*inv(x*x' + CPD.prior.n)*x;
alpha = CPD.prior.alpha;
L = log_student_pdf(y, x'*CPD.prior.theta, f*alpha/CPD.prior.beta, 2*alpha);
else
error('can''t handle batch data');
end
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